Document Type

Article

Publication Date

7-2015

Publication Title

Transactions of the Mathematical Society

Volume

368

Issue

4

Publisher

American Mathematical Society

Abstract

We define toric partial orders, corresponding to regions of graphic toric hyperplane arrangements, just as ordinary partial orders correspond to regions of graphic hyperplane arrangements. Combinatorially, toric posets correspond to finite posets under the equivalence relation generated by converting minimal elements into maximal elements, or sources into sinks. We derive toric analogues for several features of ordinary partial orders, such as chains, antichains, transitivity, Hasse diagrams, linear extensions, and total orders.

Comments

This manuscript has been published in the journal Transactions of the Mathematical Society. Please find the published version here (note that a subscription is necessary to access this version):

http://www.ams.org/journals/tran/2016-368-04/S0002-9947-2015-06356-9/home.html

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